Simpkins Corporation does not pay any dividends because it is expanding rapidly and needs to retain all of its earnings. However, investors expect Simpkins to begin paying dividends, with the first dividend of $0.75 coming 3 years from today. The dividend should grow rapidly - at a rate of 70% per year - during Years 4 and 5. After Year 5, the company should grow at a constant rate of 6% per year. If the required return on the stock is 13%, what is the value of the stock today (assume the market is in equilibrium with the required return equal to the expected return)

The current value of stock is $20.40

Explanation:

D3 = $0.75

The Growth rate for Year 4 & Year 5 is 70%. The experience after was constant growth rate (g) of 6%

D4 = $0.75 * 1.70 = $1.28

D5 = $1.28 * 1.70 = $2.18

D6 = $2.18 * 1.06 = $2.31

To get the Value of stock, r = 16%

P5 = D6 / (r - g)

P5 = $2.31 / (0.13 - 0.06)

P5 = $2.31 / 0.07

P5 = $33

P0 = $0.75/1.13^3 + $1.28/1.13^4 + $2.18/1.13^5 + $33/1.13^5

P0 = $0.75/1.4429 + $1.28/1.6305 + $2.18/1.8424 + $33/1.8424

P0 = $0.5198 + $0.7850 + $1.1832 + $17.9114

P0 = $20.3994

P0 = $20.40

So, current value of stock is $20.40

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u = 30

continuing your method

= +

subtract from both sides

= - thus

= -

= ⇒ u = 30